Three capacitors of capacitances 2 pF, 3 pF and 4 pF are connected in parallel. (a) What is the total capacitance of the combination? (b) Determine the charge on each capacitor if the combination is connected to a 100 V supply.
Given: The capacitance of the three capacitors are 2 pF,3 pF and 4 pF .
(a)
Total capacitance of the capacitor when connected in parallel is given as,
C t = C 1 + C 2 + C 3
where, total capacitance is C t , the capacitance of capacitors are C 1 , C 2 and C 3 .
By substituting the given values in the above equation, we get,
C t = 2 + 3 + 4 = 9 pF
Thus, the total capacitance of the capacitor when connected in parallel is 9 pF .
(b)
The combination is connected to 100 V supply.
The charge on the capacitor is given as,
q = C × V
where, the charge on the capacitor is q , the potential difference of each capacitor is V , the capacitance of capacitor is C .
For C 1 = 2 pF :
By substituting the given values in the above equation, we get,
q 1 = 2 × 100 = 200 pC
For C 2 = 3 pF :
By substituting the given values in the above equation, we get,
q 2 = 3 × 100 = 300 pC
For C 3 = 4 pF ":
By substituting the given values in the above equation, we get,
q 3 = 4 × 100 = 400 pC
Therefore, the charges on the capacitors are 200 pF , 3 00 pF and 4 00 pF .
Given: The capacitance of the three capacitors are
(a)
Total capacitance of the capacitor when connected in parallel is given as,
where, total capacitance is
By substituting the given values in the above equation, we get,
Thus, the total capacitance of the capacitor when connected in parallel is
(b)
The combination is connected to
The charge on the capacitor is given as,
where, the charge on the capacitor is
For
By substituting the given values in the above equation, we get,
For
By substituting the given values in the above equation, we get,
For
By substituting the given values in the above equation, we get,
Therefore, the charges on the capacitors are
